Testing for Proportional Hazards with Unrestricted Univariate Unobserved Heterogeneity

We develop tests of the proportional hazards assumption, with respect to a continuous covariate, in the presence of unobserved heterogeneity with unknown distribution at the individual observation level. The proposed tests are specially powerful against ordered alternatives useful for modeling non-proportional hazards situations. By contrast to the case when the heterogeneity distribution is known up to …nite dimensional parameters, the null hypothesis for the current problem is similar to a test for absence of covariate dependence. However, the two testing problems di¤er in the nature of relevant alternative hypotheses. We develop tests for both the problems against ordered alternatives. Small sample performance and an application to real data highlight the usefulness of the framework and methodology.

Revisiting the Dollar-Euro Permanent Equilibrium Exchange Rate: Evidence from Multivariate Unobserved Components Models

We propose an alternative approach to obtaining a permanent equilibrium exchange rate (PEER), based on an unobserved components (UC) model. This approach offers a number of advantages over the conventional cointegration-based PEER. Firstly, we do not rely on the prerequisite that cointegration has to be found between the real exchange rate and macroeconomic fundamentals to obtain non-spurious long-run relationships and the PEER. Secondly, the impact that the permanent and transitory components of the macroeconomic fundamentals have on the real exchange rate can be modelled separately in the UC model. This is important for variables where the long and short-run effects may drive the real exchange rate in opposite directions, such as the relative government expenditure ratio. We also demonstrate that our proposed exchange rate models have good out-of sample forecasting properties. Our approach would be a useful technique for central banks to estimate the equilibrium exchange rate and to forecast the long-run movements of the exchange rate.

Measuring the Euro-Dollar Permanent Equilibrium Exchange Rate using the Unobserved Components Model

This paper employs an unobserved component model that incorporates a set of economic fundamentals to obtain the Euro-Dollar permanent equilibrium exchange rates (PEER) for the period 1975Q1 to 2008Q4. The results show that for most of the sample period, the Euro-Dollar exchange rate closely followed the values implied by the PEER. The only significant deviations from the PEER occurred in the years immediately before and after the introduction of the single European currency. The forecasting exercise shows that incorporating economic fundamentals provides a better long-run exchange rate forecasting performance than a random walk process.

Age effects, unobserved characteristics and hedonic price indexes: The Spanish car market in the 1990s

This paper computes and compares alternative quality-adjusted price indexes for new cars in Spain in the period 1990-2000. The proposed hedonic approach simultaneously controls for time-invariant unobserved product e¤ects and time-variant unobserved quality changes, that are assumed to be captured by model age effects. The results show that the non-adjusted price index largely overstates the increase in the cost of living induced by changes in car prices and that previous evidence for this market have not measured the real extent of that bias, probably due to the omission of controls for unobservables. It is also shown that omitting age effects can also lead to misleading conclusions. The estimated price indexes give also some insights on what could have been the determinants of price evolution in the Spanish car market.

Age effects, unobserved characteristics and hedonic price indexes: The Spanish car market in the 1990's

This paper computes and compares alternative quality-adjusted price indexes for new cars in Spain in the period 1990-2000. The proposed hedonic approach simultaneously controls for time-invariant unobserved product effects and time-variant unobserved quality changes, that are assumed to be captured by model age effects. The results show that the non-adjusted price index largely overstates the increase in the cost of living induced by changes in car prices and that previous evidence for this market have not measured the real extent of that bias, probably due to the omission of controls for unobservables. It is also shown that omitting age effects can also lead to misleading conclusions. The estimated price indexes give also some insights on what could have been the determinants of price evolution in the Spanish car market. JEL classi…fication numbers: C43, E31, L11, L13, Keywords: Hedonic price indexes, Spanish car market, car prices, CPI, Cost of living

Unobserved heterogeneity and censoring in the demand for health care

This paper analyses the demand for private health care by Spanishhouseholds using a micro budget survey. The methodology used takescare of the three part decision process involved in this type ofbehaviour, namely the decision to use private health care, howoften to do so and how much to spend each time and also the effectsof unobserved heterogeneity. Since the theoretical frameworkcorresponds to the Grossman model of health investment, the resultsalso provide a test of the theory when these issues are considered.Finally, the obtained evidence also suggest that the current systemof tax deductions for private health care expenditures is regressive.

Female labour supply in Spain: The importance of behavioural assumptions and unobserved heterogeneity specification

We estimate four models of female labour supply using a Spanish sampleof married women from 1994, taking into account the complete form of theindividual s budget set. The models differ in the hypotheses relating tothe presence of optimisation errors and/or the way non-workers contributeto the likelihood function. According to the results, the effects of wagesand non-labour income on the labour supply of Spanish married women dependon the specification used. The model which has both preference andoptimisation errors and allows for both voluntarily and involuntarilyunemployed females desiring to participate seems to better fit the evidencefor Spanish married women.

Formal Education, Mismatch and Wages After Transition: Assessing the Impact of Unobserved Heterogeneity using Matching Estimators

This paper studies the incidence and consequences of the mismatch between formal education and the educational requirements of jobs in Estonia during the years 1997-2003. We fi nd large wage penalties associated with the phenomenon of educational mismatch. Moreover, the incidence and wage penalty of mismatches increase with age. This suggests that structural educational mismatches can occur after fast transition periods. Our results are robust for various methodologies, and more importantly regarding departures from the exogeneity assumptions inherent in the matching estimators used in our analysis

Finite-Sample Inference Methods for Simultaneous Equations and Models with Unobserved and Generated Regressors

We propose finite sample tests and confidence sets for models with unobserved and generated regressors as well as various models estimated by instrumental variables methods. The validity of the procedures is unaffected by the presence of identification problems or \"weak instruments\", so no detection of such problems is required. We study two distinct approaches for various models considered by Pagan (1984). The first one is an instrument substitution method which generalizes an approach proposed by Anderson and Rubin (1949) and Fuller (1987) for different (although related) problems, while the second one is based on splitting the sample. The instrument substitution method uses the instruments directly, instead of generated regressors, in order to test hypotheses about the \"structural parameters\" of interest and build confidence sets. The second approach relies on \"generated regressors\", which allows a gain in degrees of freedom, and a sample split technique. For inference about general possibly nonlinear transformations of model parameters, projection techniques are proposed. A distributional theory is obtained under the assumptions of Gaussian errors and strictly exogenous regressors. We show that the various tests and confidence sets proposed are (locally) \"asymptotically valid\" under much weaker assumptions. The properties of the tests proposed are examined in simulation experiments. In general, they outperform the usual asymptotic inference methods in terms of both reliability and power. Finally, the techniques suggested are applied to a model of Tobin’s q and to a model of academic performance.

Meta-analysis: a unifying meta-likelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality

OBJECTIVES: This contribution provides a unifying concept for meta-analysis integrating the handling of unobserved heterogeneity, study covariates, publication bias and study quality. It is important to consider these issues simultaneously to avoid the occurrence of artifacts, and a method for doing so is suggested here. METHODS: The approach is based upon the meta-likelihood in combination with a general linear nonparametric mixed model, which lays the ground for all inferential conclusions suggested here. RESULTS: The concept is illustrated at hand of a meta-analysis investigating the relationship of hormone replacement therapy and breast cancer. The phenomenon of interest has been investigated in many studies for a considerable time and different results were reported. In 1992 a meta-analysis by Sillero-Arenas et al. concluded a small, but significant overall effect of 1.06 on the relative risk scale. Using the meta-likelihood approach it is demonstrated here that this meta-analysis is due to considerable unobserved heterogeneity. Furthermore, it is shown that new methods are available to model this heterogeneity successfully. It is argued further to include available study covariates to explain this heterogeneity in the meta-analysis at hand. CONCLUSIONS: The topic of HRT and breast cancer has again very recently become an issue of public debate, when results of a large trial investigating the health effects of hormone replacement therapy were published indicating an increased risk for breast cancer (risk ratio of 1.26). Using an adequate regression model in the previously published meta-analysis an adjusted estimate of effect of 1.14 can be given which is considerably higher than the one published in the meta-analysis of Sillero-Arenas et al. In summary, it is hoped that the method suggested here contributes further to a good meta-analytic practice in public health and clinical disciplines.

A comparison of three different models for estimating relative risk in meta-analysis of clinical trials under unobserved heterogeneity

We focus on the comparison of three statistical models used to estimate the treatment effect in metaanalysis when individually pooled data are available. The models are two conventional models, namely a multi-level and a model based upon an approximate likelihood, and a newly developed model, the profile likelihood model which might be viewed as an extension of the Mantel-Haenszel approach. To exemplify these methods, we use results from a meta-analysis of 22 trials to prevent respiratory tract infections. We show that by using the multi-level approach, in the case of baseline heterogeneity, the number of clusters or components is considerably over-estimated. The approximate and profile likelihood method showed nearly the same pattern for the treatment effect distribution. To provide more evidence two simulation studies are accomplished. The profile likelihood can be considered as a clear alternative to the approximate likelihood model. In the case of strong baseline heterogeneity, the profile likelihood method shows superior behaviour when compared with the multi-level model. Copyright (C) 2006 John Wiley & Sons, Ltd.

Dynamics of brand competition: Effects of unobserved social networks

Brand competition is modelled using an agent based approach in order to examine the long run dynamics of market structure and brand characteristics. A repeated game is designed where myopic firms choose strategies based on beliefs about their rivals and consumers. Consumers are heterogeneous and can observe neighbour behaviour through social networks. Although firms do not observe them, the social networks have a significant impact on the emerging market structure. Presence of networks tends to polarize market share and leads to higher volatility in brands. Yet convergence in brand characteristics usually happens whenever the market reaches a steady state. Scale-free networks accentuate the polarization and volatility more than small world or random networks. Unilateral innovations are less frequent under social networks.

Redistribution with ex-ante unobserved choice

Introducing dynamics to Mirrlees' (1971) optimal taxation model creates a whole new set of issues that are only starting to be investigated in the literature. When choices are made before one's realizing her productivity incentive constraints ought to be defined as a function of more complex strategies than in the static case. 80 far, all work has assumed that these choices are observable and can be contracted upon by the government. Here we investigate choices that : i) are not observed, andj ii) affect preferences conditional Oil the realization of types. In the simplest possible model where a non-trivial filtration is incorporated we show how these two characteristics make it necessary for IC constraints to be defined in terms of strategies rather than pure announcements. Tax prescriptions are derived, and it is shown that they bear some resemblance to classic optimal taxation results. We are able to show that in the most 'natural' cases return on capital ought to be taxed . However, we also show that the uniform taxation prescription of Atkinson and Stiglitz fails to hold, in general.

Can unobserved heterogeneity in farmer ability explain the inverse relationship between farm size and productivity?

The well-known inverse relationship between farm-size and productivity is usually explained in terms of diminishing returns with respect to land and other inputs coupled with various types of market frictions that prevent the efficient allocation of land across farms. We show that even if in the absence of diminishing returns one can provide an alternative explanation for this phenomenon using endogenous occupational choice and heterogeneity with respect to farming skills.